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Jan. 19, 2005
Cars and Motorcycles
A repair shop fixes both cars and motorcycles. Last month, it repaired a total of 40 vehicles. The total number of wheels on those vehicles was 100.
How many cars and how many motorcycles were repaired?
MathGolf: Challenge 17
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Assume that each of the cars had four wheels and each of the motorcycles had two wheels.
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There were 10 cars and 30 motorcycles.
If all 40 vehicles were motorcycles, the total number of wheels would be 80. That would be 20 fewer wheels than the total on the vehicles actually repaired.
Replacing a single motorcycle by a car increases the total number of wheels by two, and the difference decreases by two.
Hence, 10 such replacements are required for the difference to be reduced to zero.
10 x 4 + 30 x 2 = 100.
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